MrC is exactly right. You would pay 100K in interest over the 15 yrs with zero down. With 20% down you would pay 80K in interest.
http://www.bankrate.com/calculators/...ion-calculator
Borrowing 240K, the first month your interest is $800. If you are in the 20% bracket you will get back $160 for that month essentially. By the time you are in the 60th month your interest is $580 so you get back $116, and so on--less and less as time goes on. Meanwhile you have that 240K tied up. I did not calculate this, but let's say your total mortgage deduction gets you 20K over the 15 yrs.
If you invested 240K for a return of 3% in 15 yrs you would have $376000 (compounded monthly) or with a return of 4% you'd end up with $436,000.
The thinking here is that (without taking any thing else into consideration) paying 300K up front you could save you $80K + 20K = 100K. Investing with 3% return could yield $76K and would not compensate for the 100K savings. In a better year with a return of 4% you'd earn $136K. So your crude break even point would be at between 3 and 4% return on investment (IF there were no investment fees!). If you invest well and wisely you might make more money in the long run by having a mortgage, but investing IS a risk.
But it is more complicated that that, actually, because you might want to assume you would steadily take your property payments out of the "240K pot" of investment money. This would steadily deplete that 240K you were investing, so you would never earn that lovely net of $136K - 100K = 36K. I don't have the means to calculate this but it would have a
significant effect and maybe even wipe out that 36K.